At the moment, Hostgator's default PHP version is v.5.2.4, although version 5.3 is available. Drupal 7 requires 5.3, so until they make it the default, it is necessary to manually tell Drupal where to find PHP v. 5.3. Do this by adding
Action application/x-hg-php53 /cgi-sys/php53 AddType application/x-hg-php53 .php
to an .htaccess file located in the public_html directory of your site. If Drupal is not at the root of your site, and you don't want to change the entire site over, it works just as well to modify the .htaccess file in the Drupal directory.
An .htaccess file is just a text file named ".htacess" which can contain many different types of directives understood by the apache server.
The other setting that may be necessary is to turn on the PDO extension:
extension=pdo.so extension=pdo_mysql.soto a php.ini file in the public_html (or Drupal directory, if it is not at the root of your site).
A php.ini file is a text file named php.ini which can contain many different types of settings to configure PHP on your server.